Revisited precision, recall and F1-scores for time-series.
In addition to conventional performance metrics, more recent and elaborate performance metrics tailored to time-series introduced in [1]} are considered. These metrics extend classical precision, recall, and F1-score, from point-based to range-based anomaly detection. Fig. REF  highlights the distinction between point-based and range-based anomalies. Contrary to the case of point-based approaches, a prediction in a time-series can be both a true positive (TP) and a false negative (FN) due to partial overlap with the ground-truth as shown in Fig. REF  b. Therefore, as discussed in [1]}, a more informative time-series evaluation process should (1) quantify the size of the partial overlap; (2) identify the overlap position, and; (3) take into account its cardinality, i.e., with how many anomalous ground-truth sub-sequences it overlaps. More specifically, given a set of real anomaly sequences \(R = \lbrace R_1,..., R_{Nr}\rbrace \)  and a set of predicted anomaly sequences \(P = \lbrace P_1,...,P_{N_p}\rbrace \)  the recall is expressed with respect to the number of real anomalies \(N_r\)  in a dataset [1]}. It seeks to reward a detector when it predicts a TP and penalizes it when the prediction is an FN as follows,
\({\text{Recall}_{T}(R,P)} = \frac{1}{N_r} \sum _{i = 1}^{N_r}{{\text{Recall}_T(R_i, P)}},\) 
